On the dynamics of a discrete reaction-diffusion system

We investigate various aspects of the dynamics of a discrete reaction-diffusion system. First, we examine the effect of the boundary conditions on the spatially uniform fixed point at locations far from the boundaries by using an asymptotic expansion. We show that, except for a few computational cells adjacent to the boundary, the fixed point practically coincides with the one calculated by using reflective boundary conditions (equivalent to an infinite domain). Next, we introduce a classification of the fixed points based on the wavelength in the infinite-medium approximation of the system. We use the symbolic manipulator MACSYMA to analytically calculate the amplitude of several such classes of fixed points and we generate bifurcation diagrams for their members. Also, we consider two special classes of periodic solutions; we calculate their amplitude analytically in the infinite-medium approximation, and generate bifurcation diagrams that shed new light on some previous confusing results. Finally, we present an analysis of fictitious periodic solutions that have been previously reported and incorrectly interpreted.     

A Quasilinear Hierarchical Size-Structured Model: Well-Posedness and Approximation

A finite difference approximation to a hierarchical size-structured model with nonlinear growth, mortality and reproduction rates is developed. Existence-uniqueness of the weak solution to the model is established and convergence of the finite-difference approximation is proved. Simulations indicate that the monotonicity assumption on the growth rate is crucial for the global existence of weak solutions. Numerical results testing the efficiency of this method in approximating the long-time behavior of the model are presented.     

Further Studies with Ethyl 5‐Amino‐3‐phenyl‐lH‐pyrazole‐4‐carboxylate1

The newly synthesized ethyl 3‐amino‐5‐phenylpyrazole‐4‐carboxylate 1 was diazotized and coupled with β‐naphthol, active methylene reagents 6 , 9 , 12 , 15 , and the active methine 19 to afford the pyrazolo[5,1‐c]triazines 5 , 8 , 11 , 14 , 17 , 18 , and the pyrazolo[5,1‐ c ]‐1,2,4‐triazoles 21 , 22 , and 23 , respectively. Structures are elucidated and mechanisms are discussed.     

A discrete two-stage population model: continuous versus seasonal reproduction

A discrete two-stage model which describes the dynamics of a population where juveniles and adults compete for different resources is developed. A motivating example is the green tree frog (Hyla cinerea) where tadpoles and adult frogs feed on separate resources. First, continuous breeding is assumed and the asymptotic behavior of the resulting autonomous model is fully analyzed. It is shown that the unique interior equilibrium is globally asymptotically stable when the inherent net reproductive number is greater than one. However, when the inherent net reproductive number is less than one, the population becomes extinct. Then a seasonal breeding described by a periodic birth rate with period 2 is assumed. It is proved that for this nonautonomous model a period two solution is globally asymptotically stable when the inherent net reproductive number is greater than one and when the inherent net reproductive number is less than one the population becomes extinct. Finally, the advantage (in terms of maximizing the number of juveniles and adults in the population over a fixed time period) of having a seasonal breeding is studied by comparing the average of the juvenile and adult numbers of the periodic solution for the nonautonomous model to the equilibrium solution of the autonomous model. Our results indicate that for high birth rates the equilibrium of the autonomous model is higher than the average of the two cycle solution. Therefore, all other factors being equal, seasonal breeding appears to be deleterious to populations with high birth rates. However, for low birth rates seasonal breeding can be beneficial. It is also shown that for a range of birth rates the nonautnomous model is persistent while the solution to the autonomous model goes to extinction.     

A second‐order finite difference approximation for a mathematical model of erythropoiesis

We present a second‐order finite difference scheme for approximating solutions of a mathematical model of erythropoiesis, which consists of two nonlinear partial differential equations and one nonlinear ordinary differential equation. We show that the scheme achieves second‐order accuracy for smooth solutions. We compare this scheme to a previously developed first‐order method and show that the first order method requires significantly more computational time to provide solutions with similar accuracy. We also compare this numerical scheme with other well‐known second‐order methods and show that it has better capability in approximating discontinuous solutions. Finally, we present an application to recovery after blood loss. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Porous and Water Stable 2D Hybrid Metal Halide with Broad Light Emission and Selective H2O Vapor Sorption

In this work we report a strategy for generating porosity in hybrid metal halide materials using molecular cages that serve as both structure-directing agents and counter-cations. Reaction of the [2.2.2] cryptand (DHS) linker with Pb^II in acidic media gave rise to the first porous and water-stable 2D metal halide semiconductor (DHS)₂Pb₅Br₁₄. The corresponding material is stable in water for a year, while gas and vapor-sorption studies revealed that it can selectively and reversibly adsorb H₂O and D₂O at room temperature (RT). Solid-state NMR measurements and DFT calculations verified the incorporation of H₂O and D₂O in the organic linker cavities and shed light on their molecular configuration. In addition to porosity, the material exhibits broad light emission centered at 617 nm with a full width at half-maximum (FWHM) of 284 nm (0.96 eV). The recorded water stability is unparalleled for hybrid metal halide and perovskite materials, while the generation of porosity opens new pathways towards unexplored applications (e.g. solid-state batteries) for this class of hybrid semiconductors.     

Efficient One-Pot Microwave-Assisted Synthesis,Crystallographic, and Spectroscopic Characterization of Novel Antitumor and Antimicrobial (3E)-5-Hydroxy-1-Isopropyl-3-[(5-Methyl-2-Thienyl)Methylene]-5-Phenylpyrrolidin-2-One

Journal of Applied Spectroscopy - A microwave-assisted, chemoselective synthesis of novel antitumor and antimicrobial...     

A Second-Order High-Resolution Scheme for a Juvenile-Adult Model of Amphibians

In this article we consider a juvenile-adult population model of amphibians in which juveniles are structured by age and adults are structured by size. We develop a second-order explicit high-resolution scheme to approximate the solution of the model. Convergence of the finite difference approximation to the unique weak solution with bounded total variation is proved. Numerical examples demonstrate the high-resolution property and the achievement of the designed accuracy for the scheme. The scheme is then applied to understand the dynamics of an urban amphibian population.     

A high resolution finite difference method for a model of structured susceptible‐infected populations coupled with the environment

We develop a general model describing a structured susceptible‐infected (SI) population coupled with the environment. This model applies to problems arising in ecology, epidemiology, and cell biology. The model consists of a system of quasilinear hyperbolic partial differential equations coupled with a system of nonlinear ordinary differential equations that represents the environment. We develop a second‐order high resolution finite difference scheme to numerically solve the model. Convergence of this scheme to a weak solution with bounded total variation is proved. Numerical simulations are provided to demonstrate the high‐resolution property of the scheme and an application to a multi‐host wildlife disease model is explored.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1420–1458, 2017